Some Criteria For The Finiteness Of Gorenstein AC-homology Dimension

This paper mainly studies homological properties of Gorenstein AC homological modules.Firstly,we study approximations by classes of modules in which modules are either Gorenstein AC-projective or else have finite projective dimension.We construct two adjoint pairs of functors in the stable subcategories relating to the modules of finite projective dimension and Gorenstein AC-projective modules.Secondly,we define the GF₍(6（8）-closed ring and study the property of Gorenstein AC-flat modules and the modules of finite Gorenstein AC-flat dimension.